Capacitive touch screens have enabled compelling interfaces for displays. Three-dimensional (3D) sensing, where user gestures can also be sensed in the out-of-plane dimension to distances of about 20-30 cm, represents new interfacing possibilities that could substantially enrich user experience, especially with large displays. The challenge is achieving sensitivity at these distances when sensing the small capacitive perturbations caused by user interaction with sensing electrodes. Among capacitive-sensing approaches, self-capacitance enables substantially greater distance than mutual capacitance (i.e., between electrodes), but can suffer from ghost effects during multi touch. Sensing distance of such systems has still been too limited for 3D sensing. Improved techniques are needed to enable 3D sensing, particularly where gestures can be sensed in the out-of-plane dimension to distances of about 20-30 cm.